Pg.1a pg. 1b

Unit 5 Area & Volume

Area

Composite Area

Surface Area

Volume

Name:

Math Teacher:

Advanced Math 6 Unit 5 Calendar 1/7 1/8 1/9 1/10 1/11

Unit 5 Pre-Test

MSG Set Up

Unit Overview

Area of

Parallelograms,

Rectangles,

Squares and

Triangles Formula

Organizer

Area of

Composite

Figures

Area of

Composite

Figures

Quiz

IXL Skills Week of 1/7: FF.5, FF.6, FF.7 & FF.8

1/14 1/15 1/16 1/17 1/18

Nets

(Create your

own net)

Surface Area Surface Area Surface Area

Practice Quiz

IXL Skills Week of 1/14: FF.15 & FF.9

1/21 1/22 1/23 1/24 1/25

MLK Holiday Volume Volume Unit 5 Post Test

Review Test

IXL Skills Week of 1/21: FF.16 & FF.18

Pg.2a pg. 2b

Unit 5: Area & Volume Standards, Checklist and Concept Map

Georgia Standards of Excellence (GSE): GSE6.G.1: Find area of right triangles, other triangles, special quadrilaterals,

and polygons by composing into rectangles or decomposing into triangles

and other shapes; apply these techniques in the context of solving real-world

and mathematical problems

Find the area of a polygon (regular or irregular) by dividing it into

squares, rectangles, and/or triangles and find the sum of the areas of

those shapes

GSE6.G.2: Find the volume of a right rectangular prism with fractional edge

lengths by packing it with unit cubes of the appropriate unit fraction edge

lengths, and show that the volume is the same as would be found by

multiplying the edge lengths of the prism. Apply the formulas V = lwh and V =

Bh to find volumes of right rectangular prisms with fractional edge lengths in

the context of solving real-world and mathematical problems.

GSE6.G.4 : Represent three-dimensional figures using nets made up of

rectangles and triangles, and use the nets to find the surface area of these

figures. Apply these techniques in the context of solving real-world and

mathematical problems.

What Will I Need to Learn??

________ I can find the area of a polygon by splitting it up into squares,

rectangles, and/or triangles, and finding the sum of all of the areas

________ I can find the volume of a right rectangular prism with fractional

edges by packing it with unit cubes

________ I can apply the formula V = lwh to find the volume of a right

rectangular prism with fractional edge lengths

________ I can represent 3-dimensional shapes with nets

________ I can use nets to determine the surface area of 3-dimensional figures

________ I can apply these concepts of area, volume, and surface area to

solve real-world and mathematical problems

Unit 5 Circle Map: Make a Circle Map below of important vocab and topics from the

standards listed to the left.

Pg.3a pg. 3b

Unit 5 - Vocabulary Term Definition and/or Picture-Example

Area

Base (of a

triangle)

Base (of a 3D

figure)

Congruent

Cubic Units

Edge

Equilateral

Triangle

Term Definition and/or Picture-Example

Face

Isosceles Triangle

Lateral Faces

Net

Parallel

Parallelogram

Perpendicular

Pg.4a pg. 4b

Term Definition and/or Picture-Example

Polygon

Regular Polygon

Polyhedron

Prism

Pyramid

Quadrilateral

Rectangle

Rectangular

Prism

Term Definition and/or Picture-Example

Rhombus

Right Triangle

Scalene Triangle

Square

Surface Area

Trapezoid

Vertex (vertices)

Volume

Pg.5a pg. 5b

Math 6 – Unit 5: Area & Volume Review

Knowledge & Understanding

1) How could you determine the area of a composite figure,

such as the ones shown here?

2) What types of units are used to describe area?

3) What types of units are used to describe volume?

Proficiency of Skills

4) Determine the volume of the cube:

5) Find the area of the shaded section of the square:

6) Find the area of the triangle:

7) Determine the area of the trapezoid:

8) The surface area of a cube can be found by using the

formula SA = 6s2. Determine the surface area of a cube with

a length of 8cm.

9) Find the area of the figure shown below:

Application

10) If carpet costs $4 per square yard, how much would it cost

to carpet a rectangular room that is 6 yards wide and 10

yards long?

11) What is the area of the trapezoid?

1

3 cm.

9 m

25 cm

20 cm

19 cm

14

cm

1 cm 1 cm

24 cm

10 cm

5 ft

6 ft

16 ft

12 ft

Pg.6a pg. 6b

12) A rectangular prism is filled with small cubes of the same size.

The bottom layer consists of 9 cubes, each with a volume of

2 cubic inches. If there are 3 layers of cubes in the prism,

what is the volume of the rectangular prism?

13) A box is made of cardboard with no overlap. The net of the

box is shown below. How many square inches of cardboard

is needed to make the box?

14) The triangular sides of the tent are equilateral, with a base of

20 inches and a height of 15 inches. The three rectangular

sides of the tent are each 50 inches long and 20 inches

wide. What is the surface area of the tent?

15) Mariah and Max are making a plaque to dedicate to the

swaggerific saxophone players of the ECMS sixth-grade

band. The center is a 10-inch square, and the edges of the

frame measure 12 inches long and 12 inches wide. What is

the area of the frame?

16) A fish tank is shown below. What is the volume of the water

in the tank?

17) How many cubic feet are in a cubic yard?

18) The volume of a rectangular prism can be found by using

the formula V=Bh. If the base of a prism is square with a side

length of 3 inches and the height of the prism is 2 ¼ inches,

find the volume of the prism.

19) Andres is painting five faces of a storage cube (he isn’t

painting the bottom face). If each faces is 8 inches, how

many square inches will he need to paint?

20) Which of the following nets could NOT be folded to form a

cube?

a)

c)

b)

d)

8in.

1 in. 8 in.

12 ft

12 ft

5 in. 12in.

8 ½ in.

Pg.7a pg. 7b

Area of Parallelograms

Examples:

You Try:

a) b)

c) d)

Pg.8a pg. 8b

Area of Triangles

Examples:

You Try:

a) b)

c) d) e)

Pg.9a pg. 9b

Area of Trapezoids

You Try:

You Try:

d) e)

Pg.10a pg. 10b

Area of Triangles and Quadrilaterals

Area is the amount of space INSIDE a figure. It is always

measured in square units.

Triangle

𝐴 =1

2𝑏 • ℎ

B = Base

H = Height

Quadrilateral

𝐴 = 𝑙 • 𝑤 or 𝐴 = 𝑏 • ℎ

L = Length

W = Width

Example: What is the area of the triangle?

h = height = 12 m

b = base = 20 m

A = ½bh = ½ • 20 •12 = 120 m2

Example: What is the area of the rectangle?

l = length = 8cm

w = width = 3 cm

A = lw = 8 • 3 = 24 cm2

Note: A triangle is half of a rectangle. That is why the area of

a triangle is half the area of a rectangle.

You Try:

Triangle Square Rectangle

h = 6ft

b = 5ft side = 8in

l = 9cm

w = 3cm

Formula: _________

Area: ____________

Formula: _________

Area: ____________

Formula: _________

Area: ____________

How do you calculate area? Formulas for Area

Area is the _______________ of

____________ units needed to fill a

_____________________. Or, the amount

of ___________________ in a polygon.

To calculate area, you must

________________ all the _______________.

Area is always measured in

______________________________________.

Square:

Rectangle:

Triangle:

You Try:

1) When calculating

area, you can count

the square units in a

polygon.

How many square units

are there?

2) What is the area of

this shape?

3) What is the area of

this shape?

4) You can also use

the formulas above to

calculate the area of

shapes.

5) What is the area of

this shape?

6) What is the area of

this shape?

Pg.11a pg. 11b

Additional Practice with Area N

am

e o

f

Po

lyg

on

Pic

ture

Wri

te t

he

form

ula

Su

bst

itu

te fo

r th

e v

ari

ab

les

(Sh

ow

wo

rk)

So

lve

. In

clu

de

sq

ua

re

un

its

in y

ou

r a

nsw

er.

Area of Composite Figures

Pg.12a pg. 12b

The figure below is a composite figure. How would you find its

area?

The house is made up of two

shapes that you are familiar

with – a triangle and a

rectangle. You can

“decompose” or “take

apart” the figure to find the

area of each piece and then

find the sum of those areas to

get the total area.

Try This:

Find the area of the rocket figure below.

1) How many shapes can this

figure be broken into?

2) What two different types

of shapes can you see?

3) Determine the area of

each shape.

Shape Shape #1 Shape #2 Shape #3 Shape #4

Formula Area△ = ½bh

Work ½ • 16 • 4

8 • 4

Solution 32 ft2

Lastly, add the area of each piece. Total Area =

You Try:

Find the area of each composite figure. Remember to show all

work! (Hint: Often, you will have to draw in lines to decompose

the figure. Pay careful attention to the side lengths that are

given so you can figure out the side lengths that are missing!)

1)

2)

3)

1

2

4ft

4ft

6ft 16ft

14ft

5ft

3 cm

7 cm

8 cm

4 cm

14 in

12 in

22 in

10 m

3 m

3 m

2 m 6 m

Pg.13a pg. 13b

Area Error Analysis

Fill in the Flow Map with the 3 steps to solving problems on

area:

Silly Sally has struck again! Analyze her work in Column #1, and

circle her mistake. In Column #2, explain what she did wrong. In

Column #3, work out the problems correctly, showing ALL work!

Silly Sally’s Work

(Circle her mistake):

What did Silly

Sally do

wrong?

Show Silly Sally

how it’s done!

(Show ALL steps!)

A = lw

12 • 8

20 m²

A = ½ b h

½ • 4 • 6

24 cm²

A = ½ b h ½ • 8 • 9

½ • 72

8 m 36 m²

Find the area of each composite figure:

1) 2)

3) 4)

8 m

12 m

Pg.14a pg. 14b

More Area Practice with Composite Figures 1) 2)

3)

Nets

Pg.15a pg. 15b

Nets of 3-Dimensional Figures

Face is a flat _____________________ of a solid figure.

Edge is a ____________________ segment where two faces of a

____________________ meet.

Vertex is a ____________________ where ____________________ or more

edges of a solid figure meet or the pointed end of a cone opposite of

its base.

FIGURE FACES Look

Like

BASE How many

faces?

NET

Cube

Rectangular

Prism

Triangular

Prism

Square

Pyramid

Triangular

Pyramid

Cylinder

Cone

Matching Nets and 3-D Figures

Pg.16a pg. 16b

Using Formulas to Find Surface Area

A formula is a mathematical rule using variables. It allows us to

easily find a value such as area, volume, circumference,

perimeter, etc. Formulas are used often in math and science!

Formulas for Surface Area:

SA Rectangular Prism = 2(l•w) + 2(l•h) + 2(w•h)

SA Cube = 6s²

Using Formulas to Find Surface Area

So… what exactly IS surface area, anyway?

Draw a rectangular prism: Draw the net of a rectangular prism:

How do you think you could calculate the SURFACE AREA of a

RECTANGULAR PRISM?

Draw a SQARE PYRAMID: Draw the net of a SQARE PYRAMID:

How do you think you could calculate the SURFACE AREA of a SQARE

PYRAMID?

s

s

s

w l

h

Pg.17a pg. 17b

Draw a CUBE: Draw the net of a CUBE:

How do you think you could calculate the SURFACE AREA of a CUBE?

Complete the following statement:

When I need to find the surface area of a 3-dimensional (3-D)

figure, I can do that by…

You Try:

Using either method (nets or formulas), find the surface area.

1)

2) 3)

Pg.18a pg. 18b

4) 5)

6) 7) Find the Surface Area of a

cube with side length 4cm.

8) 9)

10) 11)

Pg.19a pg. 19b

Surface Area in the Real World

Solve each of the problems by drawing a net and finding the surface

area.

1) A pizza box is 15 inches wide, 14 inches long, and 2 inches tall.

How many square inches of cardboard were used to create the

box?

2) What is the surface area of a Rubik’s Cube that is 6 cm tall?

3) Angelo is making a replica of an Egyptian pyramid. He is making a

square pyramid with a base that is 3 feet long and 3 feet wide.

The triangular sides of the pyramid each have a height of 14 feet.

How much material will Angelo need to cover the pyramid?

4) Sydney is painting a rectangular toy box for her little brother.

She will paint all 4 sides and the top (she will NOT paint the

bottom). If the toy box is 20 inches tall, 12 inches wide, and

25 inches long, how many square inches will she need to

paint?

5) DeAndre is making a tent for his hamster. It is 20 cm long,

and the triangular bases are 15 cm high and 10 cm wide

(see picture below). How much material will he need to

make the tent?

20 cm

Pg.20a pg. 20b

Volume of Rectangular Prisms

Volume is the amount of space inside a 3D object, measured in

cubic units.

Volume is the _________________ of __________________ units

needed to fill the space in a three dimensional (3D) figure.

Volume is always measured in cubic units.

We calculate volume you must find the area of the ____________

then multiply it by the _____________________.

This can be written as __________ • __________.

OR __________ • __________ • __________ for a rectangular prism.

Example:

Find the volume of the rectangular prism below.

You Try:

Find the volume.

1) 2)

Ever wonder WHY volume is

measured in cubic units??

Since volume measures the amount of

space INSIDE a figure, it’s like you’re

packing the figure with little tiny cubes!!

Hence,

“cubic units”. Cool,

huh?

Here’s a visual of

a rectangular

prism being

packed with unit

cubes…

72 Cubic Units

Here’s a visual of

a cube being

packed with unit

cubes…

V = B • h

V = l • w • h

V = 4 • 4 • 6

V = 96 cm3

Pg.21a pg. 21b

3) 4)

5) Find the volume of a

rectangular prism with B =

78ft2 and h = 23 ft.

6) Find the volume of a

rectangular prism with l =

4.2cm, w = 3.8cm, and h =

6cm.

7) Find the volume of a

rectangular prism with l = 8 ¼

in., w = 9in and h = 15in.

8) Find the missing dimension of

the rectangular prism.

L = 14 cm

W = ?

H = 3 cm

V = 294 cm

Volume of Rectangular Prisms with Fractional Edges

You Try:

Find the volume of a rectangular prism with a length of 3cm, a

width of 2 ½ cm, and a height of 4 cm.

Pg.22a pg. 22b

Volume Error Analysis Sally is a silly little girl that makes silly mistakes! Analyze her work in

Column #1, and circle her mistake. In Column #2, explain what

she did wrong. In Column #3, show how Silly Sally should work out

the problem. Show ALL work!

Silly Sally’s Work

(Circle her mistake): What did Silly

Sally do wrong?

Show Silly Sally how it’s

done!

(Show ALL steps!)

More Volume Practice

Determine the Volume of each rectangular prism or cube

below. Include units and show your work!

1. A cube that is 12 yards wide

2. The box with dimensions of 6 ft • 4 ft • 1 ½ ft

3. Determine the Volume of a rectangular truck bed that is 12

feet long, 5 ¼ feet wide, and 3 feet deep.

4. How much water can be poured into a cubic tank that is 2 ½

feet long?

5. What is the volume of a gift box that is 3 ½ inches wide, 2

inches tall, and 6 inches long?

V = l w h

V = 4 • 4 • 4

V= 12 m³ 4m

8mm

2mm

1

2mm

V = l w h

V = 8 • ½ • 2

V = 4 • 2

V = 8mm2

V = l w h

V = 2

3∙

2

3∙

2

3

V = 6

9 =

2

3 in3

Cube = 2/3 in. tall

V = l w h

V = 8 ¼ • 2 ½ • 3

V = 16 1

8• 3

V = 48 1

8 yd3

8 ¼ yd

2 ½ yd

2 yd 1

1

2 yd

8 1

4 yd

V = l w h

V = 4 ½ • 1 ½ • 2

V = 8

2 •

3

2 • 2

V = 24

4 • 2

V = 12 yd3

3 yd